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Following the recent demonstration that van der Waals forces control theferroelectric ordering of layers within nanoflakes and bulk samples ofCuBiP2Se6 and CuInP2S6, it is demonstrated that they also control the internalgeometrical structure of isolated monolayers of these materials. This internalstructure involves large displacements of the copper atoms, either normal tothe layer plane or else within the plane, that change its ligation environment.In both cases, the van der Waals dispersion force out-competes traditionalbonding effects to control structure. However, we find that the aspects of thedispersion force giving rise to each effect are uncorrelated: long rangeeffects control inter-layer ferroelectric ordering whereas short-range effectscontrol internal layer structure. These conclusions are drawn consideringpredicted properties of monolayers, bilayers, and bulk materials obtained using14 density-functional-theory based methods. While the different methods usedoften predict starkly different quantitative results, they concur as to thebasic nature of ABP2X6 materials. Of the methods used, only the PBE-D3 andoptPBEvdW methods were found to predict a wide range of observed propertieswithout serious disparity. Finding optimal computational methods remains asignificant challenge for which the unusual multi-scale nature of the van derWaals interactions in ABP2X6 materials provides demanding criteria.

van der Waals forces control the internal chemical structure of monolayers within ABP2X6 lamellar materials